Exponential Regularization of EM Dyadic Green's Functions via Green's Function-induced Dirac δ-functions

摘要

In a scries of recently published contributions it was shown that singular or hyper-singular dyadic Green's functions (GFs) in computational electrostatics and electromagnetics can be utilized to construct problem-specific integral representations of the Dirac δ-function, leading to parametrized smeared out δ-functions, which tend to the Dirac δ-function for the parameter η approaching 0~+. It was also shown that the constructed δ_η-functions can be employed to regularize originating GFs associated with Poisson equation in isotropic and anisotropic dielectrics. The main result of the present paper is that the constructed δ_η-function is used to regularize dyadic GFs associated with Maxwell's equations in isotropic media. The formulae arising in the formulation arc all expressed in closed-form in spectral domain, allowing deep insights into the dynamics of the proposed regularization method. Complex media do not permit construction of GFs in closed form. Consequently, the integral representations for the δ_η-functions cannot be expressed in closed-form cither. A recipe is proposed for numerically calculating δ_η-functions in asymptotic form. This result is claimed to present a genuine contribution to the computational physics. Applications in which near field phenomena play a role, e.g., nanoscopic and plasmonic devices will benefit from the results.